The dilemma is becoming more common across the country as employers report increasing numbers of job openings. But many of those jobs are not a good fit for those who are out of work.

The reason, economists say, is that the recession accelerated the decline of some industries, such as housing construction, as others that require far different skills, including health care, emerged stronger.

Some economists predict that this disconnect is likely to grow as the economy develops jobs that require more training. President Obama, speaking last week in his State of the Union address, said the nation is facing a new "Sputnik moment" that demands a renewed focus on innovation and education to secure its economic future.

Evidence of a skills mismatch became increasingly clear in Fresno after the housing bubble burst, causing joblessness to nearly triple.

Unemployment hovers at 16.9 percent, but managers at the 7,000-employee Community Medical Centers say they cannot find enough qualified technicians, therapists, or even custodians willing and able to work with medical waste.

The situation is much the same at Jain Irrigation, which cannot find all the workers it wants for $15-an-hour jobs running expensive machinery that spins out precision irrigation tubing at 600 feet a minute, 24 hours a day, seven days a week.

"The job requires at least a high school education, and maybe some technical training, but we don't seem to be getting the right people applying," said Aric J. Olson, Jain's president.

The U.S. job market has rebounded from its July 2009 nadir, when the Labor Department reported that there were just 2.3 million job openings nationwide. (When the recession began in late 2007, there were 4.4 million openings.) In November, the latest time period covered by federal statistics, there were an estimated 3.2 million openings across the country.

But that 39 percent increase in job openings has not been accompanied by a corresponding decline in the unemployment rate, which now stands at 9.4 percent - the same as it was in July 2009.

A matter of debate

The puzzling gap between jobs and hiring has touched off a furious debate among economists, one that holds serious implications for how policymakers attack the problem.

Some economists say the persistent lack of hiring is due mostly to weak demand caused by cutbacks in household consumption and business investment. They add that though the economy is improving, job openings remain scarce: There are 4.6 jobless Americans for each opening, according to the Labor Department.